Horsepower Calculator: From Torque and RPM (and Back)

1. Choose what to solve for: horsepower, torque or engine speed.
2. Enter the other two values. Set the torque unit to lb-ft or Nm, and the power unit to HP, kW or PS.
3. Read the answer at the top, with the power shown in HP, kW and PS and the torque in lb-ft and Nm.

Torque is the twisting effort an engine makes. Horsepower is the rate at which that effort does work, so it folds in how fast the crank is spinning. An engine can make big torque at low speed yet modest power, because power needs both force and speed.

The two are tied together by engine speed. For the same torque, doubling the RPM doubles the horsepower. That is why peak power almost always sits at a higher RPM than peak torque: torque has usually started to fall by then, but rising RPM more than makes up for it.

James Watt defined the horsepower in the 1780s so he could compare his steam engines with the draft horses they replaced. One mechanical horsepower was fixed at 33,000 foot-pounds of work per minute. That single choice is where the number 5,252 comes from.

The constant 5,252 is not arbitrary. Power is torque times angular speed. One horsepower is 33,000 ft-lb per minute, and one revolution is 2 pi radians, so the conversion factor is 33,000 / (2 x pi) = 5,252.1, which rounds to 5,252.

1. Multiply torque in lb-ft by engine speed in RPM.
2. Divide by 5,252 to get mechanical horsepower.
3. To go the other way, rearrange: torque = HP x 5,252 / RPM, or RPM = HP x 5,252 / torque.

Because 5,252 appears in both the power and torque forms, the horsepower and lb-ft numbers are always equal at exactly 5,252 RPM. On any dyno chart the two curves cross at that point. For the reverse view, our torque converter handles lb-ft and Nm on their own.

Find horsepower. An engine makes 400 lb-ft at 5,252 RPM. HP = 400 x 5,252 / 5,252 = 400 hp. At exactly 5,252 RPM the two numbers match, so 400 lb-ft gives 400 hp.

Lower speed, same torque. The same 400 lb-ft would give less power lower down, and a 300 lb-ft engine at 5,000 RPM makes 300 x 5,000 / 5,252 = 285.6 hp.

Convert the power. A 400 hp rating is 400 x 0.745699872 = 298.28 kW, or about 405.6 PS. kW is the figure you will see on the registration document, while PS is common in brochures.

Find torque. If a motor is rated 400 hp at 5,000 RPM, its torque is 400 x 5,252 / 5,000 = 420.2 lb-ft (about 569.7 Nm).

The formula is exact, so the result is only as good as the two numbers you feed it. Real quoted figures vary for several reasons.

Which Horsepower

Mechanical (SAE) horsepower is 745.7 W, but metric PS is 735.5 W, about 1.4 percent smaller. A 400 PS car is about 394.5 mechanical HP, so always note which unit a brochure uses.

Crank vs Wheel

Published power is usually measured at the crankshaft. The power reaching the wheels is lower after losses in the gearbox, driveline and tyres, often by 10 to 15 percent.

Test Standard and Conditions

SAE J1349, ECE and JIS correct for air temperature, pressure and humidity in slightly different ways, so the same engine can be rated a few horsepower apart.

Torque Is Not Flat

An engine does not hold one torque value. Peak torque and peak power happen at different RPM, which is why a single calculation describes only one operating point.

Three power units describe the same thing. Knowing the factors keeps spec sheets from different markets comparable.

So 100 kW is about 134.1 HP or 136.0 PS. For the full set of power units, including watts and BTU per hour, use the power converter.

Reading a Dyno Chart

Dyno plots show torque and power against RPM. Checking that the curves cross at 5,252 RPM is a quick sanity test that the axes are right.

Comparing Engines Across Markets

Converting PS or kW to the same unit lets you line up a European and a US figure fairly.

Estimating a Missing Number

If a listing gives power and the RPM it was measured at, you can back out the torque at that point, and the other way around.

Power is only part of how a car accelerates; weight matters just as much. See how a figure translates to real pace with the 0-60 mph acceleration calculator.

1. Mixing PS with Mechanical HP

They differ by 1.4 percent. Treating 500 PS as 500 HP overstates the power by about 7 HP.

2. Putting Torque in Nm into the Lb-ft Formula

HP = torque x RPM / 5,252 only works with torque in lb-ft. Convert Nm to lb-ft first, or let this tool do it.

3. Using 5,252 with Metric Torque

With torque in Nm and speed in rad/s, power in watts is simply torque x angular speed, with no 5,252 at all. The 5,252 constant belongs to the lb-ft and RPM system.

4. Comparing Crank and Wheel Power

A chassis-dyno wheel figure is naturally lower than a crank rating. They are not the same measurement.

5. Reading Peak Torque and Peak Power Off One RPM

They occur at different engine speeds, so one calculation cannot give both peaks at once.

The arithmetic is exact. The limits are about what a single power-torque-RPM point can tell you.

Horsepower equals torque in pound-feet times RPM, divided by 5,252. Rearranged, torque = HP x 5,252 / RPM and RPM = HP x 5,252 / torque.

One horsepower is 33,000 foot-pounds of work per minute, and one revolution is 2 pi radians. Dividing 33,000 by 2 pi gives 5,252.1, which rounds to 5,252.

Because the same 5,252 constant links them. At exactly 5,252 RPM the equation makes the horsepower figure numerically equal to the lb-ft torque figure, so the two dyno curves cross there.

Multiply mechanical horsepower by 0.745699872. For example, 400 HP is 298.28 kW. To go back, divide kilowatts by that same factor.

Mechanical horsepower is 745.7 watts, while metric horsepower, or PS, is 735.5 watts. One PS equals 0.98632 HP, so PS figures read about 1.4 percent higher than mechanical HP.

Multiply pound-feet by 1.355818 to get newton metres. So 400 lb-ft is about 542.3 Nm, and dividing Nm by the same factor returns lb-ft.

It depends on the torque you enter. If you use a crank torque figure you get crank power; if you use a chassis-dyno wheel torque you get wheel power. The formula does not add or remove driveline losses.

Set the torque unit to Nm and the tool converts for you. If you do the math by hand, convert Nm to lb-ft first, because the 5,252 constant only works with lb-ft and RPM.

Not on its own. Power also depends on RPM, so a high-revving engine can make more horsepower than a higher-torque engine that spins slowly.

No. The calculation runs in your browser and nothing is sent to our servers. Anything you choose to save stays in this browser only.

• Horsepower and metric horsepower in watts, and pound-force foot in newton metres (NIST SP 811, Appendix B.9, alphabetical conversion factors).
• Conversion factors grouped by quantity, including power and torque (NIST SP 811, Appendix B.8).
• Power as the rate of doing work, the basis of the horsepower definition (NASA Glenn Research Center, Beginners Guide to Aeronautics).
• Relating horsepower, torque and rotational speed (hp = torque x rpm / 5,252) (The Engineering ToolBox, motor power, torque and speed).
• SAE J1349, the engine power test code behind quoted horsepower ratings (SAE International, J1349 Certified Power standard).